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Proof step 70 from proof bits2int-pos (previous step)

fillsgn(8, uint2bits(bits2uint(firstn(# bits0 % 8, bits0)))).first, 0 ≤ bits2uint(firstn(# bits0 % 8, bits0)), # bits0 % 8 < # bits0, # bits0 % 8 ≤ 7, 7 < # bits0, bits2uint(firstn(# bits0 % 8, bits0)) ≤ 127 ⊦ fillsgn(8, uint2bits(bits2uint(firstn(# bits0 % 8, bits0)))) = [], (# bits0 + 1) % 8 = 0, bits0 = [], fillsgn(8, uint2bits(bits2uint(firstn(# bits0 % 8, bits0)))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → (fillsgn(n, bits).first ↔ bits.first) subst: [bits, n] → [uint2bits(bits2uint(firstn(# bits0 % 8, bits0))), 8] rotate: F spec: bitopsaux inst: name: fill-first

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ¬ bits2uint(bits) < 0;% ⊦ ¬ i ≤ j ↔ j < i;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ 0 ≤ j → ¬ uint2bits(j).first; Used terms: uint2bits(bits2uint(firstn(# bits0 % 8, bits0))), 8